CHAPER 5 TEST REVIEW
Period ________ Name ______________________________
1) (2x3 + 6x2 – 5x + 11) ÷ (x + 3) =
2) (4x – 3)2 =
3) (x – 1)(x + 2)(x – 3) =
4) Factor completely: 27x3 – 125 =
5) Factor completely: x3 + 216 =
6) The volume V (in cubic feet) of an aquarium is modeled by the polynomial function V(x) = x3 + 2x2 – 13x + 10,
where x is the length of the tank.
a. Show that x – 1 is a factor of V(x) using synthetic division.
b. Factor V(x) completely.
7) Your friend has started a golf caddy business. The table shows the profits p (in dollars) of the business in the first
5 months.
Month, t 1
2
3
4
5
Profit, p
4
2
6
22
56
a. What type of polynomial is this? Use finite differences to determine.
b. Find a polynomial model for the problem. P =
c. Use the model to predict the profit after 7 months.
8) Let T be the number (in thousands) of new truck sales. Let C be the number (in thousands) of new car sales
During a 10-year period, T and C can be modeled by the following equations where t is time (in years).
T = 23t4 – 330t3 + 3500t2 – 7500t + 9000
C = 14t4 – 330t3 – 5900t + 8900
Find a new model S for the total number of new vehicle sales.
9) Describe the transformations of f represented by g.
a. f(x) = x3; g(x) = –(x – 7)3
b. f(x) = x4; g(x) = (–x)4 – 5
c. f(x) = x3; g(x) = 2(x + 3)3
d. f(x) = x3; g(x) = (5x)3
1
3
e. f(x) = x3; g(x) = ( 𝑥)3
1
10) Sketch the function f(x) = 4 (𝑥 − 1)(𝑥 + 2)(𝑥 − 3)
1
11) Sketch the function f(x) = − 3(x – 2)(x + 4)2
1
12) Sketch the function f(x) = 2(x – 5)(x – 3)2
13) Write a cubic function in factored form whose graph passes through (-4, 0), (4, 0), (0, 6), (2, 0).
14) Is the function even or odd or neither? Find out f(-x) and also look at the graph to verify.
a. f(x) = –x3 – 4x
b. f(x) = –x6 + x2
c. f(x) = x4 + 3x2 – 2
d. f(x) = x5 + 3x4
15) Let f(x) = x3 + 2. Translate 5 units to right.
16) Let f(x) = x3 + 2. Reflect in the y-axis.
17) Let f(x) = x3 + 2. Vertically stretch with a factor of 5, then reflect in the x axis.
18) Let f(x) = x3 + 2. Vertically shrink with a factor of ½, then reflect in the y-axis.
19) Let f(x) = x3 + 2. Horizontally stretch with a factor of 3.
20) Let f(x) = x3 + 2. Horizontally shrink with a factor of ½ then go up 5 units.
21) Find all zeros of f(x) = 2x3 – 7x2 – 8x + 28. Write the function in factored form.
x = ______, ________, ________
f(x) = (
)(
)(
)
22) Find all zeros of f(x) = 4x3 + x2 – 51x + 36. Write the function in factored form.
x = ______, ________, ________
f(x) = (
)(
)(
)